Dynamical invariants and intersection theory on the flex and gothic loci

Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory

10.1017/9781108608954 ◽

2020 ◽

Cited By ~ 1

Author(s):

Chris Wendl

Keyword(s):

Intersection Theory ◽

Holomorphic Curves

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Homotopical intersection theory I

Geometry & Topology ◽

10.2140/gt.2007.11.939 ◽

2007 ◽

Vol 11 (2) ◽

pp. 939-977 ◽

Cited By ~ 9

Author(s):

John R Klein ◽

E Bruce Williams

Keyword(s):

Intersection Theory

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Intersection theory and Hilbert function

Functional Analysis and Its Applications ◽

10.1007/s10688-011-0033-6 ◽

2011 ◽

Vol 45 (4) ◽

pp. 305-315

Author(s):

A. G. Khovanskii

Keyword(s):

Hilbert Function ◽

Intersection Theory

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Characteristic cohomology and observables in higher spin gravity

Journal of High Energy Physics ◽

10.1007/jhep12(2020)190 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Alexey Sharapov ◽

Evgeny Skvortsov

Keyword(s):

Higher Spin Gravity ◽

Complete Classification ◽

Gravity Models ◽

Simons Theory ◽

Surface Charges ◽

Higher Spin ◽

Dynamical Invariants ◽

Chern Simons ◽

Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

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On polytopes and generalizations of the KLT relations

Journal of High Energy Physics ◽

10.1007/jhep12(2020)057 ◽

2020 ◽

Vol 2020 (12) ◽

Cited By ~ 1

Author(s):

Nikhil Kalyanapuram

Keyword(s):

Scattering Amplitudes ◽

Large Class ◽

Moduli Space ◽

Differential Forms ◽

Natural Generalization ◽

Intersection Theory ◽

Hyperplane Arrangements ◽

Number Of Solutions ◽

Scalar Theories ◽

Double Copy

Abstract We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT). To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on ℳ0, n — the moduli space of marked Riemann spheres — the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.

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